Lab Session 13

Now try it on the training/test split

##                      ME      RMSE       MAE        MPE     MAPE      MASE
## Training set -0.3506253  8.334542  5.215022 -0.1703858 2.904052 0.2696797
## Test set     -9.7437987 13.250443 10.684962 -4.9152571 5.367077 0.5525417
##                    ACF1 Theil's U
## Training set 0.03921138        NA
## Test set     0.23659054 0.6344392

Lab Session 16

## Series: train 
## ARIMA(1,1,0)(1,1,0)[12] 
## Box Cox transformation: lambda= -0.2741334 
## 
## Coefficients:
##           ar1     sar1
##       -0.2188  -0.3834
## s.e.   0.0539   0.0510
## 
## sigma^2 estimated as 0.0001804:  log likelihood=960.12
## AIC=-1914.23   AICc=-1914.16   BIC=-1902.82
## Series: train 
## ARIMA(3,1,0)(2,1,0)[12] 
## Box Cox transformation: lambda= -0.2741334 
## 
## Coefficients:
##           ar1      ar2     ar3     sar1     sar2
##       -0.2192  -0.0053  0.1307  -0.5164  -0.3482
## s.e.   0.0552   0.0559  0.0545   0.0527   0.0523
## 
## sigma^2 estimated as 0.0001574:  log likelihood=982.76
## AIC=-1953.51   AICc=-1953.26   BIC=-1930.68
## ETS(M,Ad,M) 
## 
## Call:
##  ets(y = train) 
## 
##   Smoothing parameters:
##     alpha = 0.8031 
##     beta  = 0.0049 
##     gamma = 1e-04 
##     phi   = 0.9767 
## 
##   Initial states:
##     l = 63.945 
##     b = 0.2145 
##     s = 0.9895 0.9373 1.0084 1.1736 1.0097 1.0174
##            0.9782 0.9979 0.9931 0.9466 0.9759 0.9725
## 
##   sigma:  0.0457
## 
##      AIC     AICc      BIC 
## 3383.427 3385.526 3452.611

## 
##  Ljung-Box test
## 
## data:  Residuals from Seasonal naive method
## Q* = 1256.8, df = 24, p-value < 2.2e-16
## 
## Model df: 0.   Total lags used: 24

## 
##  Ljung-Box test
## 
## data:  Residuals from Holt-Winters' multiplicative method
## Q* = 43.167, df = 8, p-value = 8.171e-07
## 
## Model df: 16.   Total lags used: 24

## 
##  Ljung-Box test
## 
## data:  Residuals from ETS(M,Ad,M)
## Q* = 40.992, df = 7, p-value = 8.126e-07
## 
## Model df: 17.   Total lags used: 24

## 
##  Ljung-Box test
## 
## data:  Residuals from STL +  ETS(M,A,N)
## Q* = 91.221, df = 20, p-value = 4.531e-11
## 
## Model df: 4.   Total lags used: 24

## 
##  Ljung-Box test
## 
## data:  Residuals from ARIMA(3,1,0)(2,1,0)[12]
## Q* = 54.96, df = 19, p-value = 2.357e-05
## 
## Model df: 5.   Total lags used: 24
## [1] 23.40458
## [1] 59.85277
## [1] 25.43061
## [1] 34.82789
## [1] 105.5313